Given the functions $f(x) = 2x + 1$ and $g(x) = x^2 + 2x + 1$, we need to find $(f \circ g)(-2)$.

Step-by-Step Solution

1. Calculate $g(-2)$: $g(x) = x^2 + 2x + 1$ Substitute $x = -2$: $g(-2) = (-2)^2 + 2(-2) + 1$ $= 4 - 4 + 1$ $= 1$

2. Calculate $f(g(-2)) = f(1)$: $f(x) = 2x + 1$ Substitute $x = 1$: $f(1) = 2(1) + 1$ $= 2 + 1$ $= 3$

Thus, $(f \circ g)(-2) = 3$

Summary:

$(f \circ g)(-2) = 3$

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Related Questions:

1. What is $(g \circ f)(-2)$?
2. Find the inverse of $g(x)$.
3. Calculate $(f \circ g)(0)$.
4. Determine $(f \circ f)(2)$.
5. What is the range of $g(x)$?
6. Find the derivative of $f(x)$.
7. Calculate $g(-1)$.
8. Determine the critical points of $f(x)$.

Tip:

Always check the domain of the inner function before substituting it into the outer function in composite functions.